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The Anna Karenina Principle

Tolstoy began the novel Anna Karenina as follows: All happy families are alike; each unhappy family is unhappy in its own way. This statement can easily be extended from fiction to reality and from family dynamics to other fields. In the case of forensic engineering, it might be phrased: all successful structures are alike; each failure occurs in its own way. It is surprisingly easy to state what is necessary for a structure to be successful. Its strength and serviceability need to remain intact under the loads to which is subjected. That’s all. Seeing that it happens is a bit more difficult than say it.

There are, per Tolstoy, an infinite number of ways that failures can occur. Fortunately for those of us looking to understand them, they generally fall into a limited number of categories. The category of failure that haunts structural engineers, improper design, is easy to understand in theory but often hard to show. One of the most commonly-occurring categories, failure to translate the design properly into physical reality, was written up in yesterday’s New York Times with regard to the horrific collapse of an elevated metro line in Mexico City last month. The article is quite long and details any number of problems with the process of design, construction, and administration of the train line, but focusses on one issue regarding the collapse: the failure of welds connecting shear studs to the steel girders at the overpass that collapsed.

Reinforced-concrete is inherently a composite material, using the embedded steel in tension to strengthen concrete, which is weak in tension. Prior to the early 1900s, steel was used as a solo material; but starting (in the US, anyway) in the 1920s, people developed a way to improve steel construction using composite action. Steel is strong in tension but has a tendency to buckle in compression, so why not flip the idea of reinforced-concrete around, and use concrete to carry some or all of the compression for steel? Simply adding concrete would be a terrible idea, but if there was concrete already present – in the form of floor slabs in steel-framed buildings, or deck slabs in steel bridges – all you have to do is connect the two in a manner that creates some non-obvious load paths. (For the engineers in the crowd: the shear flow along the steel/concrete interface created by analyzing the steel and concrete as a composite beam.) Shear studs have been, from the 1950s onward, the most common way to provide that connection. They look like bolts without threads, steel rods with cylindrical heads, and are welded at their bottom to the top flanges of beams before the concrete slabs are cast over the top.

The evidence suggests that the studs on the metro bridge were not welded properly and had irregular spacing. the problem with the welds is obvious. There problem with the spacing is that it would interfere with the proper composite action even if the welds were working. The most damning detail in the article is that ceramic ferrules were still present on many of the studs. These are small donuts put around the base of the studs during the welding process to keep the molten metal in places and help shape it into a proper connection between the beam flange and the stud. They are supposed to be removed when the welding is complete, which is easily done because they are resistant to thermal damage but brittle and can be broken away by hand. Their presence in the final concrete is not bad because the weaken the connection. They do, slightly, but not remotely enough to cause a failure. The problem is that it is not possible to properly inspect the weld if the ferrule is present. Since the failure seems to have been precipitated by failure of the welds, knowing that they were badly inspected, or not inspected at all, seems critical. It’s important to note that improper welds are a technical failure while improper inspection is a management failure.

A year ago I wrote a blog post about the sinking of the General Slocum, one of the worst incidents in US history in terms of loss of life not triggered by a natural disaster. As with the Mexico City metro, there was an underlying technical flaw – the size of the porthole windows – surrounded by human failures.